Given f(x)=3^x-2 and g(x)=f(3x)+4, write the function rule for function g and describe the types of transformations that occur between function f and function g

g(x) = 3^(3x-2)+ 4

transformations: horizontal compression and vertical translation

Step-by-step explanation:

Given

f(x)=3^(x-2)

To get f(3x) replace x by 3x:

f(3x) = 3^[(3x)-2] = 3^(3x-2)  

Add 4 to that result and get g(x):

g(x)=f(3x)+4 = 3^(3x-2)+ 4

g(x) has two parts, 'f(3x)' and '+ 4'

f(3x) -> horizontal compression by a factor of 3

+ 4 -> vertical translation up 4 units

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